Question 25350: Larry, Mo, and Curly wish to mow 5900 square foot lawn. Larry can mow 70 square feet per minute, Mo can mow 50 square feet per minute, and Curly can mow 40 square feet per minute. Mo and Curly begin mowing, but Larry has problems starting his mower and begins 30 minutes later. All three stop mowing when the lawn is finished. How long does Larry mow?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Moe and Curly start moeing, I mean mowing, at the same time. The lawn is getting
mowed at the sum of their rates.
The two of them are the only ones mowing until Larry starts 30 minutes later.
So far, I have this equation:
(1) ft2 of lawn mowed = (Moes rate in ft2/min)+(Curly's rate in ft2/min)*(time elapsed)
plugging in the numbers:
(2) ft2 of lawn mowed = (50 ft2/min + 40 ft2/min)x 30 min
ft2 of lawn mowed = 2700 ft2
Then 30 minutes have elapsed, Larry starts mowing. Now I need a new equation.
(3)ft2 of lawn left to mow / (Moe's rate + Curly's rate + Larry's rate) = time
Note that this equation is much like:
Distance / rate = time
Equation (1) was like:
Distance = rate x time
(4) ft2 of lawn left to mow / (50 ft2/min + 40 ft2/min + 70 ft2/min) = Larry's time
Note that the time here is the time period after Moe and Curly have been
mowing for thirty minutes and Larry started mowing at 70 ft2/min.
(5) (5900 ft2 - 2700 ft2) / 160 ft2/min = Larry's time
(6) 3200 ft2 / 160 ft2/min = Larry's time
(7) 20 min = Larry's time
So Larry mowed for 20 minutes. Moe and Curly, by the way, mowed for 30 min + 20 min = 50 min
So, I can check:
((50 ft2/min + 40 ft2/min)x 50 min) + ((70 ft2/min)x 20 min = size of lawn
4500 ft2 + 1400 ft2 = 5900 ft2
it checks
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